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Properties

Label 3150.2.dq
Level $3150$
Weight $2$
Character orbit 3150.dq
Rep. character $\chi_{3150}(169,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1440$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3150.dq (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3150, [\chi])\).

Total New Old
Modular forms 5824 1440 4384
Cusp forms 5696 1440 4256
Eisenstein series 128 0 128

Trace form

\( 1440 q - 180 q^{4} + 16 q^{5} - 8 q^{9} + O(q^{10}) \) \( 1440 q - 180 q^{4} + 16 q^{5} - 8 q^{9} + 8 q^{11} - 20 q^{12} - 8 q^{14} + 20 q^{15} + 180 q^{16} + 4 q^{20} - 48 q^{25} - 24 q^{29} + 16 q^{30} - 24 q^{31} - 16 q^{36} + 12 q^{39} + 16 q^{44} + 144 q^{45} + 100 q^{47} + 40 q^{48} + 720 q^{49} - 4 q^{50} + 40 q^{51} + 48 q^{54} - 24 q^{55} + 8 q^{56} - 12 q^{59} + 16 q^{60} + 20 q^{63} + 360 q^{64} + 152 q^{65} + 60 q^{67} - 68 q^{69} - 80 q^{71} + 160 q^{74} + 40 q^{78} + 8 q^{80} - 16 q^{81} - 24 q^{85} + 40 q^{86} + 300 q^{87} - 160 q^{89} - 60 q^{90} + 60 q^{92} + 12 q^{95} + 88 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3150, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)